A typical case in which a wall support element is introduced into a section of a tubular structure lies in the medical field, when blood vessels constricted by stenoses need to be kept open with the aid of a so-called “stent”, i.e. a vascular prosthesis, or when they need to be lined in the event of an aneurysm in order to prevent the aneurysm from bursting. In this context, FIG. 1 shows the treatment of a carotid stenosis as an example. A carotid stenosis is a constriction of the carotid artery supplying the brain. It occurs owing to pathological modifications of the vessel wall, often connected with hardening. In the scope of an endovascular treatment of such a stenosis, a catheter K is initially guided into the vessel G as far as the lesion L, i.e. as far as the constriction (see FIG. 1, left). A folded stent S is then brought to the constriction by means of the catheter K (see FIG. 1, middle) and expanded there. The expansion presses the thickened sites outward as far as possible, so that an acceptable diameter is again achieved in the interior of the vessel G (see FIG. 1, right).
In order to select the appropriate stent for the individual case in question, before fitting the stent it would be expedient to carry out a simulation which is adapted as far as possible to the current situation, i.e. the vessel in question and the size and nature of the lesion. Methods for simulating the placement of stents in blood vessels are described, for example, in DE 10 2006 058 908 A1 and DE 10 2007 039 207 A1. A wireframe model of a stent is fitted virtually into the vessel, the model of the vessel structure having been generated with the aid of image data from an imaging method, for example with a magnetic resonance tomograph or a computer tomograph. The model of the vessel structure is rigid in this simulation method. Precisely in the case of a stent simulation, however, it is expedient to be able to simulate the behavior of highly coiled vessels which can be smoothed by placement of the stent. In this way, the stent dimensions of the selected stent can be assessed better in advance even in such complicated cases. To this end, it is helpful when the behavior or deformation of the vessel wall can also be taken into account in the simulation.
The publication “Finite Element Analysis of Stent Expansion Considering Stent, Artery and Plaque Interaction” by S. M. Kim and S. Y. Park in Proceedings of the 24th IASTED International Conference on Biomedical Engineering, 143-146, 2006, describes a simulation method in which the interaction between the stent and the artery, as well as the plaque, are analyzed with the aid of a finite element method. In the method described there, very elaborate reconstructed models of the stent and the arteries are required. Furthermore, the dissertation by H. Y.-C. Huang, “Theoretical and Experimental Modelling of Stress within the Neck of Endoluminal Grafted Artery”, University of New South Wales, 2006, describes a way of compiling an elastic vessel model and thereby modeling the stent/vessel wall interaction during a stent expansion in the scope of a finite element method. Here, nonlinear mathematical models are developed for different arteries. The development of the models is likewise extraordinarily time-consuming, more than one day of computer time sometimes being required for one model.
The methods mentioned above are therefore very useful, for example for developing new stents or checking already existing stents. For patient-specific simulation in situ before introducing a stent, for example to assist in the selection of a stent suitable for the current case, these methods are however unsuitable owing to the time they take.